1. (40 points) Consider the system in the figure below, where the z axis will be aligned with the downward sloping plane. Between the entrance and exit points, the fluid is flowing due to gravity. Entrance disturbance. Liquid film - Liquid in Reservoir Exit disturbance B Direction of Z gravity The coordinate system is identified in the figure ( you MUST use this system). The fluid/plate interface is at x = 0, the fluid/air interface is x = 8 and z is the direction of flow. Note that the y direction is coming out of the page. The dimensions of the flow tray are: 0 >>>>>>> than 8.Make the following assumptions: i. Steady state, fully developed flow ii. Incompressible fluid iii. NO pressure change in any direction iv. Gravity vector acts in the direction noted on the figure and is constant v. The fluid is moving in the z direction. Thus, the velocity vector is v =[0,0,vz] vi. Negate edge effects or changes in the velocity with respect to z or y, thus v #f(y, z) vii. Shear at the fluid-air interface (x = 8) can be assumed to be zero Questions: 1. List all team members 2. Draw a control volume (CV) for system and State the general Conservation of Momentum (COM)Equation. 3. Complete the left-hand side of the COM balance by assessing the Sum of Forces acting on a CV within the illustrated system. X component: Y component: Z component: 4. Complete the right-hand side of the COM equation by balancing the momentum accumulation and/or ux and applying the assumptions. 5. Generate the nal COM equation. 6. Solve to nd the general solution for the In 7. Apply the shear boundary condition (outlined in the assumption section) to nd the unique solution for In (as I have not given you the actual values for the gravitational constant or the angle ,8, you should still have those constants in your nal unique solutions) 8. Apply the assumption that the uid is Newtonian and solve to nd the general solution for V2 9. Apply the boundary condition to nd the unique solution for V2 10. Bonus (4 points): What is the average velocity for V2